Question

1. Are all of the individual independent variables significant? (Use a level of significance of 0.05 to conduct your tests). State the null and alternative hypotheses, the test statistic critical and calculated values and the conclusion for each independent variable. (mpg dependent variable, independent variables wt, disp, hp)
2. Based on the results from parts b and c would you suspect that multicollinearity might be a problem in this case? Support your answer by computing the variance inflation factors for each of the explanatory (independent) variables in your model.

mpg	disp	hp	wt
21	160	110	2.62
21	160	110	2.875
22.8	108	93	2.32
21.4	258	110	3.215
18.7	360	175	3.44
18.1	225	105	3.46
14.3	360	245	3.57
24.4	146.7	62	3.19
22.8	140.8	95	3.15
19.2	167.6	123	3.44
17.8	167.6	123	3.44
16.4	275.8	180	4.07
17.3	275.8	180	3.73
15.2	275.8	180	3.78
10.4	472	205	5.25
10.4	460	215	5.424
14.7	440	230	5.345
32.4	78.7	66	2.2
30.4	75.7	52	1.615
33.9	71.1	65	1.835
21.5	120.1	97	2.465
15.5	318	150	3.52
15.2	304	150	3.435
13.3	350	245	3.84
19.2	400	175	3.845
27.3	79	66	1.935
26	120.3	91	2.14
30.4	95.1	113	1.513
15.8	351	264	3.17
19.7	145	175	2.77
15	301	335	3.57
21.4	121	109	2.78

Answer 1

1. The hypothesis being tested is:

H0: β1 = 0

H1: β1 ≠ 0

The p-value is 0.9285.

Since the p-value (0.9285) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that the slope is significant.

The hypothesis being tested is:

H0: β2 = 0

H1: β2 ≠ 0

The p-value is 0.0110.

Since the p-value (0.0110) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the slope is significant.

The hypothesis being tested is:

H0: β3 = 0

H1: β3 ≠ 0

The p-value is 0.0013.

Since the p-value (0.0013) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the slope is significant.

variables	coefficients	std. error	t (df=28)	p-value
Intercept	37.1055
disp	-0.0009	0.0103	-0.091	.9285
hp	-0.0312	0.0114	-2.724	.0110
wt	-3.8009	1.0662	-3.565	.0013

2. There is no problem of multicollinearity.

variables	VIF
Intercept
disp	7.325
hp	2.737
wt	4.845